Why?
Battles other than sieges can already end in under a minute of actual fighting due to how quickly men are killed once they meet.
That's a separate issue totally, and has no bearing on the current discussion IMO. The battle AI fights like amateur gangs, instead of trained men in formations. It's an AI issue, not an armor-vs-bows issue.
A lot of the time flanking is redundant because the extra seconds (and I do mean seconds) spent maneuvering means they kill fewer men than the press of bodies in the middle or the shooting gallery of archers from the back.
This is also largely irrelevant, because it's a behavioral problem (if there is one.)
The armor already has significant defensive effect in battle, against arrows. Compared to reality, the archers already let loose from shorter distances than in real life, and while high-angle shooting behavior is introduced in game, they don't use volley fire. The "AoE carpet bombing" is already weaker than it actually is in real life, not to mention the distance causes a significant drop off in damage. Unless you are using the strongest of bows, even the nearly unarmored looters take more than 2 shots kill when the distance is far enough (unless a lucky head shot.) You can test this out yourself -- how many are you able to kill with a single arrow at a distance of over 150? You'd be hard pressed to even hit the target, unless using some sort of cheat or trainer to correct aiming.
The distances where the archers, and their arrows become really threatening, is as you approach under 100 distance in game. And particularly going under 70~80 the archers fire direct targeted shots. Under 50, each shot become significantly lethal. And under those distances, arrows are known to penetrate most armor of the era, barring the highest quality steel lamellar or scale.
There really isn't any grounds to say archers are OP in the first place. Yes, the damage system (in all practicality) does not allow for "failed to penetrate" shots from happening, which is unrealistic, but at the same time, none of the arrows hinder a troops capability to fight, whereas in real life a single penetrated shot to the torso is almost guaranteed to either kill on impact, or at least immobilize immediately. So the relative balance is pretty even.
If you want the armor to be strengthened to realistic standards and have high-grade armor literally deflect arrows with 0 damage, without any counterbalancing for the bows/arrows, then all that is going to do is just make ranged fire useless in the game -- because players don't build realistic armies. Players just hoard t4-5-6 troops, which means all of them will be just immune to arrow fire.